Part 1: Find the Eigenfunction Expansion Consider the function f (same as in the previous problem) defined on the interval [0, 10] as follows, 3 x, f(x)= x = [0,5], 5 3. x = [5, 10]. Find the coefficients C, of the eigenfunction expansion of function f, 00 f(x) = co+cn Yn(x), where yo=1 (which is not a unit eigenfunction), while yn, for n = 1, 2, 3, ., are unit the eigenfunctions of the Regular Sturm-Liouville system -y" = Ay. y' (0) = 0, y' (10) = 0. Note: The constant eigenfunction yo= 1 is not a unit eigenfunction, since yo yo = 10. Therefore, the formula for co is co= the eigenfunctions yn, for n = 1, 2, 3, ... to be unit eigenfunctions. Therefore, the formula for the coefficients c, is C = fyn- f-yo We choose yo yo Σ Co= Σ Cn =

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